There are many known ways for detecting whether a sequence of a certain number of bits (also called “data frame” or simply “frame”) includes erroneous bits due to errors during transmission or storage of a data frame. One common way is to include further data bits in the data frame which represent a check sum (also called hash sum). For example, a single parity bit may represent a very simple check sum. However, more sophisticated procedures (so called hash functions) for calculating check sums are known. Another common example for a hash function which may be used for generating check sums is called “cyclic redundancy check” (CRC) or “polynomial code checksum.” Dependent on the order of the polynomial which is in such a procedure, it is referred to as CRC4, CRC12, CRC64, etc. (i.e., a CRC using a polynomial of order 4, 12, 64, etc.). For example data transmissions via an Ethernet network or transmissions from and to a hard drive are checked by CRC methods.
Different CRC procedures using polynomials of different lengths (generally different check sum methods) are typically associated with a certain probability that a received bit is incorrect but not detected. One application in which bit errors may have fatal consequences are electronic control units (ECUs) that control the deployment of the airbags installed in an automobile. In such applications the probability of an undetected bit error (bit error probability) and the bit error rate are closely related to the probability of an accidental deployment of an airbag which may have fatal consequences. For this reason the relevant standards such as ISO 26262 (titled “Road vehicles—Functional safety”) define so-called “safety integrity levels” (e.g., ASIL A to ASIL D, whereby ASIL is short for “automotive safety integrity level”) which are associated with different upper limits for the probability of failures dependent on the risk related to such failure.
In view of the extremely high requirements for the detection of errors in transmitted data frames, particularly in automotive applications, there is a need for improved methods and systems allowing for a reliable data transmission.